Four homeless people have died of exposure on the streets of Portland, Oregon, in the first 10 days of 2017, a toll that has horrified the city and focused attention on its housing crisis.

“Any loss of life is unacceptable,” the newly inaugurated Portland mayor, Ted Wheeler, said. “This is a wealthy nation and we’re a prosperous and progressive community.”

According to police and local media, David Guyot, 68, was found at a bus stop, taken to the hospital and died on the first day of the month. Mark Elliot Johnson, 51, died on an East Portland sidewalk on 2 January. Karen Lee Batts, 52, was found in a downtown parking garage on 7 January after being evicted from her low-income housing unit, where she had $338 of unpaid rent. And an unidentified 29-year-old male was discovered on Tuesday in a wooded area on a south-west Portland hillside.

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Portland has faced an unusually brutal winter, with temperatures dropping into the teens with record snowfall. It is also struggling with low vacancy rates and a lack of affordable housing. A 2015 count found that there were 3,800 homeless people in the city, and like many in the western US it has been engulfed by a sense of emergency over the problem.

“Gone are the days when a west coast mayor can be content with filling potholes and making sure the streets are safe. Now it’s about addressing the large issues facing America,” Wheeler said.

Wheeler plans to dedicate much of his tenure to mental health, housing affordability and homelessness issues, and the city recently passed a $260m affordable housing bond.

In response to the cold weather, Wheeler has taken the unprecedented move of converting the city’s administrative building into a shelter, and he has opened up hundreds of emergency beds.

Although he vowed nobody would be turned away from a shelter, obstacles remain for some who are looking for a dry place to rest at night.

LaKeisha Tillman, 37, lugged her red suitcase and two black garbage bags through the city’s snowy and nearly empty streets recently. She had been sleeping by railroad tracks and was making her way to a church, which she found to be closed. She relies on a walker and said traipsing around the city is difficult.

Exposure is not the only danger facing the city’s homeless residents. In 2015, nearly 90 people died on the streets of the city and the broader Multnomah County, said Israel Bayer, who runs Street Roots, a weekly newspaper that serves the homeless population. There was a wide range of causes, including alcohol and drug abuse, suicide and natural causes. But this year the elements have proved particularly uncompromising.

“The cold weather has expedited and created a nightmare scenario,” he said. “It is unprecedented to have four people freeze to death on the streets of Portland in such a short period of time.”

Bayer was not willing to point fingers over the deaths. “We should all be held accountable,” he said.